Question

The escape speed from the moon is much smaller than from earth. True or False

Answer 1

True

The escape speed from the Moon is much smaller than from Earth.

Step-by-step explanation:

The escape speed is defined as:

`v_(e) = \sqrt{(2GM)/(r)}` (1)

Where G is the gravitational constant, M is the mass and r is the radius.

The mass of the Earth is
`5.972x10^(24)kg` and its radius is
`6371000m`

Then, replacing those values in equation 1 it is gotten.

`v_(e) = \sqrt{((2)(6.67x10^(-11)N.m^(2)/kg^(2))(5.972x10^(24)kg))/((6371000m))}`

`v_(e) = 11.18m/s`

For the case of the Moon:

`v_(e) = \sqrt{((2)(6.67x10^(-11)N.m^(2)/kg^(2))(7.347x10^(22)Kg))/((1737000m))}`

`v_(e) = 2.38m/s`

Hence, the escape speed from the Moon is much smaller than from Earth.

Since it has a smaller mass and smaller radius compared to that from the Earth.